Our main site, accountabilitymn.org, doesn't have any speed issues and loads 4x times as fast and is built on drupal.

I want to test the youclaimit.org site on Dreamhost, which offers free hosting for nonprofits, but I need to pay a developer to do this for us. Before I can get the approval for this, I know my supervisor will want to know why one site is having speed issues when the other is not. I'm not familiar with how hosting works and wouldn't know what to say, could someone please help me out here?